Former Palestinian Foreign Minister Mahmoud el-Zahar and former Interior Minister Saeed Seyam held talks with Egyptian intelligence chief Omar Suleiman, Egypt's main contact with the Palestinian Islamist movement Hamas and Israel, the Egyptian state news agency MENA said.
A Palestinian official close to the talks said the Hamas delegation would tell Suleiman it is prepared to accept the idea of a staged truce, starting with Gaza only.
"Hamas' position is that they agree to a calm in Gaza and the West Bank but it would begin in Gaza at this stage and then apply to the West Bank after an agreed and specified period of time," said the official, who declined to be named.
Hamas, which controls Gaza but has prominent members in the West Bank, has previously insisted that a truce should begin and apply at the same time to both areas.
Israel said it was ready for "quiet" at the Gaza border, but that it would require a halt to attacks by Hamas on Israelis, a stop to cross-border rocket fire from all Palestinian groups and an end to weapon smuggling into Gaza.
"We can't have a period of quiet that will just be the quiet before the storm," said Mark Regev, spokesman for Israeli Prime Minister Ehud Olmert.
The Palestinian official said Hamas made any truce conditional on Israel opening all of Gaza's border crossings and halting military action in the territory.
The Islamist group had backing from other Palestinian militant factions in the enclave, he added.
Egypt would relay Hamas' proposal to Israel in the coming days, he added. Israeli officials said they were skeptical about the chances of reaching a cease-fire in the Gaza Strip.
"We are not holding our breath," a senior Israeli official said. "We certainly don't want Hamas to have an interval to get stronger."
Israel has said it is not negotiating a truce with Hamas but would have no reason to launch attacks on the Gaza Strip if rocket fire from the territory ceased. But it says it reserves the right to take military action to protect its citizens.
The Egyptian intelligence chief, who is in regular contact with the Israelis, has been trying to negotiate a truce between Israel and Hamas, especially since Palestinians broke through the border with Egypt in January to escape a long Israeli siege.
Former U.S. President Jimmy Carter, on a Middle East tour which ended this week, tried to persuade Hamas to declare a unilateral ceasefire with Israel. Hamas declined on the grounds that Israel had not responded to similar gestures in the past.
Dozens of Palestinians have been killed in Israeli attacks on Gaza in the past 10 days. Three Israeli soldiers were killed on the Gaza border on April 16.
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